Is it permissible to give zakat to poor parents who live in their son's house and are supported by him, and who own an old house that they plan to sell for Hajj? Is it permissible to give zakat to a divorced sister who has a compensation for alimony of $4,000 and relies on her brothers for her livelihood? Is it permissible to give zakat to a married sister who has two children and whose husband works for a monthly salary of $400 and they live without paying rent?

Zakat (definition) is only given to the eight categories (of recipients). Your relative may give zakat to your parents if they are poor and your and your brother’s financial support is insufficient for them. Regarding selling the house for Hajj, it is not obligatory to sell one's primary residence for Hajj unless there is an extra house beyond one's needs, and the conditions of istita'ah (ability) are met. As for the money your sister saves, she must pay zakat on it if it reaches the nisab (definition) (minimum threshold) and a hawl (full lunar year) has passed over it. It is not permissible to give her zakat if she is financially self-sufficient with her money. The distinguishing limit for wealth that prevents one from receiving zakat is that a person finds sufficiency for a year. So, if your sister's money is not enough for her expenses for a year, and her father is unable to complete her expenses, then it is permissible to give her zakat. However, it is not permissible to give zakat to a married sister if she is self-sufficient through her husband's financial support.